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This paper presents an original approach for learning models, partially known, of particular interest when performing source identification or structural health monitoring. The proposed procedures employ some amount of knowledge on the system under scrutiny as well as a limited amount of data efficiently assimilated.

Two different formulations are explored. The first, based on the use of informed neural networks, leverages data collected at specific locations and times to determine the unknown source term of a parabolic partial differential equation. The second procedure, more challenging, involves learning the unknown model from a single measured field history, enabling the localization of a region where material properties differ.

Both procedures assume some kind of sparsity, either in the source distribution or in the region where physical properties differ. This paper proposed two different neural approaches able to learn models in order to perform efficient inverse analyses.

Two original methodologies are explored to identify hidden property that can be recovered with the right usage of data. Both methodologies are based on neural network architecture.